Binding theory (e.g., Chomsky, 1981) has played a central role in both syntactic theory and models of language processing. Its constraints are designed to predict that the referential domains of pronouns and reflexives are nonoverlapping, that is, are complementary; these constraints are also thought to play a role in online reference resolution. The predictions of binding theory and its role in sentence processing were tested in four experiments that monitored participants' eye movements as they followed spoken instructions to have a doll touch a picture belonging to another doll. The instructions used pronouns and reflexives embedded in picture noun phrases (PNPs) containing possessor phrases (e.g., Pick up Ken. Have Ken touch Harry's picture of himself). Although the interpretations assigned to pronouns were generally consistent with binding theory, reflexives were frequently assigned interpretations that violated binding theory. In addition, the timing and pattern of eye movements were inconsistent with models of language processing that assume that binding theory acts as an early filter to restrict the referential domain. The interpretations assigned to reflexives in PNPs with possessors suggest that they are binding-theory-exempt logophors, a conclusion that unifies the treatment of reflexives in PNPs.